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Modeling of the time-resolved vibronic spectra of polyatomic molecules: the formulation of the problem and analysis of kinetic equations

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 Added by Sergey Astakhov
 Publication date 2002
  fields Physics
and research's language is English




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A semiempirical parametric method is proposed for modeling three-dimensional (time-resolved) vibronic spectra of polyatomic molecules. The method is based on the use of the fragment approach in the formation of molecular models for excited electronic states and parametrization of these molecular fragments by modeling conventional (one-dimensional) absorption and fluorescence spectra of polyatomic molecules. All matrix elements that are required for calculation of the spectra can be found by the methods developed. The time dependencies of the populations of a great number (>10^3) of vibronic levels can be most conveniently found by using the iterative numerical method of integration of kinetic equations. Convenient numerical algorithms and specialized software for PC are developed. Computer experiments showed the possibility of the real-time modeling of three-dimensional spectra of polyatomic molecules containing several tens of atoms.



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Recently a number of diatomic and polyatomics molecules has been identified as a prospective systems for Doppler/Sisyphus cooling. Doppler/Sisyphus cooling allows to decrease the kinetic energy of molecules down to microkelvin temperatures with high efficiency and then capture them to molecular traps, including magneto-optical trap. Trapped molecules can be used for creation of molecular fountains and/or performing controlled chemical reactions, high-precision spectra measurements and a multitude of other applications. Polyatomic molecules with heavy nuclei present considerable interest for the search for new physics outside of Standard Model and other applications including cold chemistry, photochemistry, quantum informatics etc. Herein we would like to attract attention to radium monohydroxide molecule (RaOH) which is on the one hand an amenable object for laser cooling and on the other hand provides extensive possibilities for searching for P-odd and P,T-odd effects. At the moment RaOH is the heaviest polyatomic molecule proposed for direct cooling with lasers.
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At any resolution level of wavelet expansions the physical observable of the kinetic energy is represented by an infinite matrix which is ``canonically chosen as the projection of the operator $-Delta/2$ onto the subspace of the given resolution. It is shown, that this canonical choice is not optimal, as the regular grid of the basis set introduces an artificial consequence of periodicity, and it is only a particular member of possible operator representations. We present an explicit method of preparing a near optimal kinetic energy matrix which leads to more appropriate results in numerical wavelet based calculations. This construction works even in those cases, where the usual definition is unusable (i.e., the derivative of the basis functions does not exist). It is also shown, that building an effective kinetic energy matrix is equivalent to the renormalization of the kinetic energy by a momentum dependent effective mass compensating for artificial periodicity effects.
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